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Bertrand's box paradox: A paradox of conditional probability closely related to the Boy or Girl paradox. Bertrand's paradox: Different common-sense definitions of randomness give quite different results. Birthday paradox: In a random group of only 23 people, there is a better than 50/50 chance two of them have the same birthday.
This category contains paradoxes in mathematics, but excluding those concerning informal logic. "Paradox" here has the sense of "unintuitive result", rather than "apparent contradiction". "Paradox" here has the sense of "unintuitive result", rather than "apparent contradiction".
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités (1889) [1] as an example to show that the principle of indifference may not produce definite, well-defined results for probabilities if it is applied uncritically when the domain of possibilities is infinite.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
All horses are the same color is a falsidical paradox that arises from a flawed use of mathematical induction to prove the statement All horses are the same color. [1] There is no actual contradiction, as these arguments have a crucial flaw that makes them incorrect.
In 2020, it was announced that Google's AlphaFold, a neural network based on DeepMind artificial intelligence, is capable of predicting a protein's final shape based solely on its amino-acid chain with an accuracy of around 90% on a test sample of proteins used by the team.
Galileo's paradox is a demonstration of one of the surprising properties of infinite sets. In his final scientific work, Two New Sciences, Galileo Galilei made apparently contradictory statements about the positive integers. First, a square is an integer which is the square of an integer.
A falsidical paradox establishes a result that appears false and actually is false, due to a fallacy in the demonstration. Therefore, falsidical paradoxes can be classified as fallacious arguments: The various invalid mathematical proofs (e.g., that 1 = 2) are classic examples of this, often relying on a hidden division by zero.